Solutions For System Of Equations Research Articles

An investigation of the solutions for rational systems of difference equations of order two

An investigation of the solutions for rational systems of difference equations of order two

Multiplicity results of periodic solutions for a coupled system of wave equations

Multiplicity results of periodic solutions for a coupled system of wave equations

Numerical Solutions for Fractional Multi-Group Neutron Diffusion System of Equations

Numerical Solutions for Fractional Multi-Group Neutron Diffusion System of Equations

Existence and uniqueness of Carathéodory and Filippov solutions for discontinuous systems of differential equations

Existence and uniqueness of Carathéodory and Filippov solutions for discontinuous systems of differential equations

Исследование периодических решений системы обыкновенных дифференциальных уравнений с квазиоднородной нелинейностью

The article considers a system of ordinary differential equations in which the main nonlinear part, which is a quasi-homogeneous mapping, is distinguished. The question of the existence of periodic solutions is investigated. Consideration of a quasi-homogeneous mapping allows us to generalize previously known results on the existence of periodic solutions for a system of ordinary differential equations with the main positively homogeneous non-linearity. An a priori estimate for periodic solutions is proved under the condition that the corresponding unperturbed system of equations with a quasi-homogeneous right-hand side does not have nonzero bounded solutions. Under the conditions of an a priori estimate, the following results were obtained: 1) the invariance of the existence of periodic solutions under continuous change (homotopy) of the main quasi-homogeneous non-linear part was proved; 2) the problem of homotopy classification of two-dimensional quasi-homogeneous mappings satisfying the a priori estimation condition has been solved; 3) a criterion for the existence of periodic solutions for a two-dimensional system of ordinary differential equations with the main quasi-homogeneous non-linearity is proved.

Characterizations of entire solutions for the system of Fermat-type binomial and trinomial shift equations in ℂ n#

Abstract In this article, we investigate the existence and the precise form of finite-order transcendental entire solutions of some system of Fermat-type quadratic binomial and trinomial shift equations in C n {{\mathbb{C}}}^{n} . Our results are the generalizations of the results of [H. Y. Xu, S. Y. Liu, and Q. P. Li, Entire solutions for several systems of nonlinear difference and partial differential-difference equations of Fermat-type, J. Math. Anal. Appl. 483 (2020), 123641, 1–22, DOI: https://doi.org/10.1016/j.jmaa.2019.123641.] and [H. Y. Xu and Y. Y. Jiang, Results on entire and meromorphic solutions for several systems of quadratic trinomial functional equations with two complex variables, RACSAM 116 (2022), 8, DOI: https://doi.org/10.1007/s13398-021-01154-9.] to a large extent. Most interestingly, as a consequence of our main result, we have shown that the system of quadratic trinomial shift equation has no solution when it reduces to a system of quadratic trinomial difference equation. In addition, some examples relevant to the content of the article have been exhibited.

Finding And Comparing Solutions For An Undetermined System Of Linear Equations Using Scilab: Minimum-Norm Solution And Consistency Analysi

Finding And Comparing Solutions For An Undetermined System Of Linear Equations Using Scilab: Minimum-Norm Solution And Consistency Analysi

Extension of the Optimal Auxiliary Function Method to Solve the System of a Fractional-Order Whitham–Broer–Kaup Equation

In this paper, we introduce and implement the optimal auxiliary function method to solve a system of fractional-order Whitham–Broer–Kaup equations, a class of nonlinear partial differential equations with broad applications in mathematical physics. This method provides a systematic and efficient approach to finding accurate solutions for complex systems of fractional-order equations. We give a full analysis using tables and figures to demonstrate the reliability and accuracy of our approach. We confirm the effectiveness of our suggested method in solving the considered equations using numerical simulations and comparisons, emphasizing its potential for applications in a variety of scientific and engineering areas.

Estimates of matrix solutions of operator equations with random parameters under uncertainties

We investigate problems of estimating solutions of linear operator equations with random parameters under conditions of uncertainty. We establish that the guaranteed rms estimates of the matrices are found as solutions of special optimization problems under certain observations of the system state. As the output signals of the system, we have observations that are described by linear functions from the solutions of such equations with random right-hand sides, which have unknown second moments. Under the condition that the observation second moments of the right-hand parts and errors belong to certain sets, it is proved that the guaranteed estimates are expressed through solutions of operator equation systems. When the linear operator is given by the scalar product of rectangular matrices, a quasi-minimax estimate and its error are constructed. It is shown that the quasi-minimax estimation error tends to zero when the number of observations tends to infinity. An example of calculating the guaranteed rms estimate of the matrix's trace, which is a solution of a matrix equation with a random parameter, is given.

Existence of mild solutions for a coupled system of fractional evolution equations via Mönch's fixed point theorem in Banach spaces

Existence of mild solutions for a coupled system of fractional evolution equations via Mönch's fixed point theorem in Banach spaces

A Hybrid Method for All Types of Solutions of the System of Cauchy-Type Singular Integral Equations of the First Kind

In this note, the hybrid method (combination of the homotopy perturbation method (HPM) and the Gauss elimination method (GEM)) is developed as a semi-analytical solution for the first kind system of Cauchy-type singular integral equations (CSIEs) with constant coefficients. Before applying the HPM, we have to first reduce the system of CSIEs into a triangle system of algebraic equations using GEM, which is then carried out using the HPM. Using the theory of the bounded, unbounded and semi-bounded solutions of CSIEs, we are able to find inverse operators for the system of CSIEs of the first kind. A stability analysis and convergent of the proposed method has been conducted in the weighted Lp space. Moreover, the proposed method is proven to be exact in the Holder class of functions for the system of characteristic SIEs for any type of initial guess. For each of the four cases, several examples are provided and examined to demonstrate the proposed method’s validity and accuracy. Obtained results are compared with the Chebyshev collocation method and modified HPM (MHPM). Example 3 reveals that the error term of the MHPM is slightly superior to that of the HPM. One of the features of the proposed method is that it can be solved as a complex-valued system of CSIEs. Numerical results revealed that the hybrid method dominates others.

Periodic Solutions for an Impulsive System of Fractional Order Integro-Differential Equations with Maxima

Periodic Solutions for an Impulsive System of Fractional Order Integro-Differential Equations with Maxima

Influence of strong solar proton events on propagation of radio signals in the VLF range in a high-latitude region

In this paper, we examine the features of RSDN-20 signal propagation in a high-latitude Earth–ionosphere waveguide during solar proton events, using computational experiment methods. We have analyzed two proton ground-level enhancement (GLE) events of December 13, 2006 (GLE70) and September 10, 2017 (GLE72). Electron density profiles were constructed using the Global Dynamic Model of Ionosphere (GDMI) and the RUSCOSMICS model, developed at PGI. We present estimated phase and amplitude changes in RSDN-20 signals during precipitation of high-energy protons in the high-latitude region of the Earth–ionosphere waveguide. From the results of computational experiments and the analysis of the electromagnetic signal attenuation based on analytical Maxwell’s equation system solution in magnetized ionospheric plasma, we have found a pattern in the signal attenuation frequency dependence associated simultaneously with the signal reflection height, electron density profiles, and the collision frequency of electrons with neutral particles and ions. We discuss limitations of the computational experiment method and compare simulation results with data from Lovozero and Tuloma observatories.

Влияние сильных солнечных протонных событий на распространение радиосигналов в диапазоне ОНЧ в области высоких широт

In this paper, we examine the features of RSDN-20 signal propagation in a high-latitude Earth–ionosphere waveguide during solar proton events, using computational experiment methods. We have analyzed two proton ground-level enhancement (GLE) events of December 13, 2006 (GLE70) and September 10, 2017 (GLE72). Electron density profiles were constructed using the Global Dynamic Model of Ionosphere (GDMI) and the RUSCOSMICS model, developed at PGI. We present estimated phase and amplitude changes in RSDN-20 signals during precipitation of high-energy protons in the high-latitude region of the Earth–ionosphere waveguide. From the results of computational experiments and the analysis of the electromagnetic signal attenuation based on analytical Maxwell’s equation system solution in magnetized ionospheric plasma, we have found a pattern in the signal attenuation frequency dependence associated simultaneously with the signal reflection height, electron density profiles, and the collision frequency of electrons with neutral particles and ions. We discuss limitations of the computational experiment method and compare simulation results with data from Lovozero and Tuloma observatories.

Stochastic finite volume method for uncertainty quantification of transient flow in gas pipeline networks

We develop a weakly intrusive framework to simulate the propagation of uncertainty in solutions of generic hyperbolic partial differential equation systems on graph-connected domains with nodal coupling and boundary conditions. The method is based on the Stochastic Finite Volume (SFV) approach, and can be applied for uncertainty quantification (UQ) of the dynamical state of fluid flow over actuated transport networks. The numerical scheme has specific advantages for modeling intertemporal uncertainty in time-varying boundary parameters, which cannot be characterized by strict upper and lower (interval) bounds. We describe the scheme for a single pipe, and then formulate the controlled junction Riemann problem (JRP) that enables the extension to general network structures. We demonstrate the method's capabilities and performance characteristics using a standard benchmark test network.

Existence of Solutions for a Coupled System of Nonlinear Implicit Differential Equations Involving $$\varrho $$-Fractional Derivative with Anti Periodic Boundary Conditions

Existence of Solutions for a Coupled System of Nonlinear Implicit Differential Equations Involving $$\varrho $$-Fractional Derivative with Anti Periodic Boundary Conditions

Analysis of Implicit Solutions for a Coupled System of Hybrid Fractional Order Differential Equations with Hybrid Integral Boundary Conditions in Banach Algebras

This paper investigates the existence and uniqueness of implicit solutions in a coupled symmetry system of hybrid fractional order differential equations, along with hybrid integral boundary conditions in Banach Algebras. The methodology centers on a hybrid fixed-point theorem that involves mixed Lipschitz and Carathéodory conditions, serving to establish the existence of solutions. Moreover, it derives sufficient conditions for solution uniqueness and establishes the Hyers–Ulam types of solution stability. This study contributes valuable insights into complex hybrid fractional order systems and their practical implications.

Results on Solutions for Several Systems of Partial Differential-Difference Equations with Two Complex Variables

This article is to describe the entire solutions of some partial differential-difference equations and systems. Some theorems about the forms of transcendental entire solutions with finite order for several high-order partial differential-difference equations (or systems) of the Fermat type with two complex variables are obtained. Moreover, some examples are provided to explain that our results are precise to some extent.

The Diophantine problem for systems of algebraic equations with exponents

Consider the equation q1αx1+…+qkαxk=q, with constants α∈Q‾∖{0,1}, q1,…,qk,q∈Q‾ and unknowns x1,…,xk, referred to in this paper as an algebraic equation with exponents. We prove that the problem to decide if a given equation has an integer solution is NP-complete, and that the same holds for systems of equations (whether α is fixed or given as part of the input). Furthermore, we describe the set of all solutions for a given system of algebraic equations with exponents and prove that it is semilinear.

Global Existence and Decay Rate of Smooth Solutions for Full System of Partial Differential Equations for Three-Dimensional Compressible Magnetohydrodynamic Flows

We focus on the global existence andLp−Lqrates of convergence for the compressible magnetohydrodynamic equations inR3. We prove the global existence of smooth solutions using the standard energy method under the condition that the initial data are close to a constant equilibrium state inH3. Rates of convergence for the solution inLqnorm with2≤q≤6and its first- and second-order derivatives inL2norm are obtained, if the initial data belong toLpwith1≤p≤65.